Where can I get music downloads on my Linux computer?
you can download music from Amazon right from Rhytmbox or Amarok (it's part of KDE Software Compilation but can installed without mess on Unity Ubuntu)
Does not matter, if you have linux, mac or windows.
you will have to buy/download them from websites,
for example : albums featured on makeuseof
It depends where you want to download the music from. Although you can't use it to download, Spotify is available on Linux natively now.